Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature

Zhongxian Cao

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arXiv · 2511.16128

Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature

Zhongxian Cao

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Abstract

Let $(M^5,g)$ be a five-dimensional non-trivial simply-connected compact quasi-Einstein manifold with boundary. If $M$ has constant scalar $R$, Johnatan Costa, Ernani Ribeiro Jr, and Detang Zhou show that $R$ = $((m-5)k+20)/(m-k+4)\lambda$ for some $k\in\{0,2,3,4\}$. Both cases of $k=0$ and $k=4$ are already classified. In this paper we will prove that the case $k=3$ is rigid.

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Zhongxian Cao. 2025-11-20. Rigidity of five-dimensional quasi-Einstein manifolds with constant scalar curvature. https://arxiv.org/abs/2511.16128

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